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   Aimiuwu, Godstand; Khan, Faiz; Mualen, David; Tang, Wei-Ting; Brunelli, Nicholas A; Paulson, Joel A; Winter, Jessica O; Wyslouzil; Barbara (July 2025, Chemical engineering journal)

   Rapid mixing is a critical step in many nanoparticle syntheses that can impact the ability to scale production from bench to industrial levels. This study combines experimental and computational approaches to characterize mixing dynamics in crossflow jet mixing reactors (JMRs) with millimeter-scale internal dimensions. The Villermaux-Dushman reaction system is used to quantify experimental mixing times across different reactor sizes and flow rates. Complementary computational fluid dynamics (CFD) simulations assess changes in the state of the flow and estimate mixing times under varying operating conditions. Mixing times derived from CFD results agree well with the experimental results for mixing indices between 0.95 and 0.98. To demonstrate the impact of mixing on nanoparticle formation, we synthesize polybutylacrylate-b-polyacrylic acid (PBA-PAA) block co-polymer nanoparticles, confirming the existence of a critical flow rate beyond which particle size stabilizes. Additionally, we produce polylactic acid-co-glycolic acid (PLGA) nanoparticles incorporating a hydrophobic dye, achieving an average particle size below 300 nm at a throughput of ∼ 1.3 kg/day. These results provide insights into optimizing JMRs for high-throughput, reproducible nanoparticle synthesis, bridging the gap between benchtop and industrial-scale production. 

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2. Dissipation enhancement by mixing

   https://doi.org/10.1088/1361-6544/ab0e56  

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   https://doi.org/10.1103/PhysRevE.109.014606  

   Mitchell, Kevin A.; Sabbir, Md Mainul; Geumhan, Kevin; Smith, Spencer A.; Klein, Brandon; Beller, Daniel A. (January 2024, Physical Review E)

   Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) “topological entropy”—the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments. 

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4. Mixing Estimates for Estuaries

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5. Mixing Surfaces, Algebra, and Geometry

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   Margalit, Dan (May 2023, Notices of the American Mathematical Society)